summing two 3d matrices to check convergence

Given two 3d matrices, obtained in a iterative process as the solution to a PDE, I want to check convergence. To do so, I check:

abs( sum( A(:) - Aold(:) ) ) < eps

Is this the best way to do it? I mean, if I declare

A = rand(100,200,50);
B = rand(100,200,50);

And if I check

check1 = abs( sum( A(:)-B(:) ) );
check2 = abs( sum(sum(sum( A-B ) ) ) );
check3 = abs( sum(A(:)) - sum(B(:)) );
check4 = abs( sum(sum(sum(A))) - sum(sum(sum(B))) );

They should give the same answer. However,

>> check1-check2

ans =

     2.3306e-12

>> check1-check3

ans =

     3.8846e-09

>> check1-check4

ans =

    -2.4812e-10

>> check2-check3

ans =

     3.8823e-09

>> check2-check4

ans =

    -2.5045e-10

>> check3-check4

ans =

    -4.1327e-09

So it clearly is not exactly the same thing. What is the difference between the methods and what is the difference between sum(A(:)) and sum(sum(sum(A))) ? If I want to check convergence on a iterative process, what is the best way to do it?

[Matt J]

I think you really meant

sum(abs(A(:)-Aold(:)))<eps

This is the same as my Answer below, with p=1.

Answer 1

[Matt J]

 norm(A(:)-Aold(:),p)<eps

where you choose p corresponding to your favorite p-norm